Eigenvalues Of A Fredholm Integral Operator And Applications To Problems Of Statistical Inference

. We determine the eigenvalues of a Fredholm integral operator of the second kind. The solution of the eigenvalue problem has applications to finding the distribution function of a stochastic integral. The stochastic integral itself represents the asymptotic form of a statistical test. Also discussed are related results for inference and applications. 1. Introduction. Applications of Fredholm integral operators in the areas of physical sciences and engineering are well known. Their applications to problems of statistical inference are probably less known among researchers in mathematics and other disciplines. The dynamic instability inherent in physical processes can often be statistically modelled by the change-point method. The change-point problem primarily consists of testing for a model with no change in the model parameters against a model where parameter changes occur after a certain unknown point of time. The problem has received wide attention among researchers in statistical ..

Residual partial sum limit process for regression models with applications to detecting parameter changes at unknown times

Limit processes for sequences of stochastic processes defined by partial sums of linear functions of regression residuals are derived. They are Gaussian and are functions of standard Brownian motion. Cramér-von Mises type functionals defined on the partial sum processes are shown to converge in distribution to the same functionals defined on the limit processes. This result is then applied to derive the asymptotic forms of two-sided change detection statistics for linear regression models. These are derived for a variety of weight sequences and are shown to involve sums of Cramér-von Mises type stochastic integrals. Finally a methodology is developed to derive distributions of these stochastic integrals for the case of harmonic regression. This methodology is applicable to more general situations.residual process change-point problem stochastic integrals harmonic regression

Fast algorithms for the electromagnetic simulation of planar structures

This paper reviews the state of the art in fast integral equation techniques for solving large scale electromagnetic radiation and compatibility problems. The Fast Multipole Method (FMM) and its frequency and time domain derivatives are discussed. These techniques permit the rapid evaluation of fields due to known sources and hence accelerate the solution of boundary value problems arising in the analysis of a wide variety of electromagnetic phenomena. Specifically, the application of the Steepest Descent Fast Multipole Method (SDFMM) and the Thin Stratified medium Fast Multipole Algorithm (TSM-FMA) to the frequency domain analysis of radiation from microstrip structures residing on finite and infinite substrates and ground planes, respectively, is described. In addition, the extension of the FMM concept to Plane Wave Time Domain (PWTD) algorithms that permit the analysis of transient phenomena is outlined.link_to_subscribed_fulltex